Stage-structured Population Research Articles

Asymmetric interactions and their consequences for vital rates and dynamics: the smaller tea tortrix as a model system

Asymmetric interactions among conspecifics can have diverse effects on population dynamics including stabilization, generation of cycles, and induction of chaotic fluctuations. A difficult challenge, however, is establishing the link between the impact of asymmetric interactions on life history and the consequences for population dynamics. The smaller tea tortrix, Adoxophyes honmai, is a good example. Larval instars differ dramatically in size and have a tendency for cannibalism, which suggests the potential for strong asymmetric interactions among instars. Yet whether these asymmetries have any role in generating the distinct single-generation cycles observed in the field and laboratory is unclear. Here we report on the development of a new experimental approach to characterize the impact of asymmetric interactions on life history that can be directly embedded into stage-structured population models. The experiments use donor-replacement protocols in which focal individuals are challenged to complete their life cycles in competitive environments where the instar and density of the competitors are held constant. The experimentally derived interaction surface contains all the information about stage-specific interactions and provides a straightforward framework for evaluating alternative ways of abstracting the interactions into traditional models of asymmetric competition. Working with the smaller tea tortrix, we found strong evidence of asymmetric interactions and identified critical "tipping points" in the competitive environment that strongly affected survival but not development. We incorporated the experimentally derived interaction surface into a stage-structured population model and found that despite the strong impact that asymmetric interactions have on tea tortrix life history, they do not scale-up to impact the predicted asymptotic population dynamics. Comparing these dynamics with two abstracted models of stage-structured interactions revealed that while the quantitative details of the emergent dynamics depends on the shape of the interaction surface, the qualitative features, such as the emergence of single-generation cycles and rapid synchronization of development among individuals, are pleasingly robust.

Persistence and spread of stage-structured populations in heterogeneous landscapes.

Conditions for population persistence in heterogeneous landscapes and formulas for population spread rates are important tools for conservation ecology and invasion biology. To date, these tools have been developed for unstructured populations, yet many, if not all, species show two or more distinct phases in their life cycle. We formulate and analyze a stage-structured model for a population in a heterogeneous habitat. We divide the population into pre-reproductive and reproductive stages. We consider an environment consisting of two types of patches, one where population growth is positive, one where it is negative. Individuals move randomly within patches but can show preference towards one patch type at the interface between patches. We use linear stability analysis to determine persistence conditions, and we derive a dispersion relation to find spatial spread rates. We illustrate our results by comparing the structured population model with an appropriately scaled unstructured model. We find that a long pre-reproductive state typically increases habitat requirements for persistence and decreases spatial spread rates, but we also identify scenarios in which a population with intermediate maturation rate spreads fastest.

Contraception of prepubertal young can increase cost effectiveness of management of overabundant koala populations

Context With limited resources for wildlife management and conservation, it is vital that the effectiveness of management programs is maximised and costs reduced. Koala populations need to be reduced in locations where they are locally overabundant and over-browsing their food trees. Subcutaneous contraceptive implants containing levonorgestrel are currently used to control koala fertility to assist in reducing population densities. Dependent young are caught with their mothers, so are also available for contraception. Aims The overall aim was to investigate whether the effectiveness of koala contraception programs can be improved by administering levonorgestrel implants to female young along with their mothers. This was achieved by: (1) determining if implanting females before sexual maturation affects their fertility, growth and pouch development; and (2) developing a stage-structured population growth model to compare two management scenarios. Methods Juvenile female koalas (11–17 months old) were treated with either a control (n = 5) or 70 mg levonorgestrel implant (n = 5). Koalas were caught every 4 to 6 weeks for 15 months, then every 3 to 12 months for 5 years. Koalas were weighed and head length measured. Pouches were checked for young. Pouch development was assessed as a proxy for sexual maturation. A stage-based population model simulating koala population growth was developed to compare different management scenarios: no treatment; treatment of adults only; and treatment of adults plus their dependent young. Key results Levonorgestrel implants prevented births with no effect on growth, survival or timing of sexual maturation. Population growth simulations indicate that treating dependent young with their mothers results in earlier population reduction. Conclusions The treatment of prepubertal female koalas with levonorgestrel implants is a safe and effective method that increases the effectiveness of koala contraception programs. Implications Development of novel strategies may provide opportunities to increase the efficiency and cost-effectiveness of management programs with constrained resources.

Growing Trend in Application of Age-Stage, Two-Sex Life Table Theory in Diverse Ecological and Pest Management Studies

Life table is an effective tool for characterizing the demography of an arthropod to understand the phenomenon in pest population development which is a key for developing IPM strategy. Age-stage, two-sex life tables provide comprehensive insights into the stage differentiation of an arthropods, compared with the traditional female age-specific life tables and any other forms of life tables. The age-stage, two-sex life table approach is applied in diverse type of ecological and pest management research. This article is intended to draw attention of Nepalese researchers towards the significance of demographic studies for development of IPM strategy, advancements in application of age-stage, two-sex life table approach and its computer programs. Altogether more than 694 peer reviewed papers and PhD theses have been published since 1988. Out of this, 92 papers were sampled and reviewed for this paper. In such papers, demography of diverse 50 species of arthropods classified under 27 different families belonging to 10 orders have been studied using this theory to measure their fitness in diverse food and environment condition, to assess their consumption, predation or parasitism capacity and to project their population growth in different scenario, to forecast the timing of control based on the stage structure of pest populations and to be used in mass rearing and harvesting of predators and preys under biological control program.

Slow recovery from a disease epidemic in the spotted hyena, a keystone social carnivore

Predicting the impact of disease epidemics on wildlife populations is one of the twenty-first century’s main conservation challenges. The long-term demographic responses of wildlife populations to epidemics and the life history and social traits modulating these responses are generally unknown, particularly for K-selected social species. Here we develop a stage-structured matrix population model to provide a long-term projection of demographic responses by a keystone social predator, the spotted hyena, to a virulent epidemic of canine distemper virus (CDV) in the Serengeti ecosystem in 1993/1994 and predict the recovery time for the population following the epidemic. Using two decades of longitudinal data from 625 known hyenas, we demonstrate that although the reduction in population size was moderate, i.e., the population showed high ecological ‘resistance’ to the novel CDV genotype present, recovery was slow. Interestingly, high-ranking females accelerated the population’s recovery, thereby lessening the impact of the epidemic on the population.

Numerical Simulation of Leslie-Gower Predator-Prey Model with Stage-Structure on Predator

In this paper, we introduce Leslie-Gower predator-prey model with a stage-structure population on the predator. This model consists of two populations, that are prey and predator populations. Here, we divide predator into two stages. Thus, we have three classes of population in this model that are prey, juvenile predator, and mature predator. The focus of this paper is to know the interaction between the population that is affected by stage-structure in predator population in the model and to study numerically the effects of stage-structure in predator population on the interaction of prey and predator. It is found that the transition rate from juvenile to mature predator is a very important parameter which may determine the long-term behavior of both prey and predator. Keywords: Leslie-Gower model, predator-prey model, stage-structure.

Dynamics of a stage-structured single population model with state-dependent delay

In this paper, a novel stage-structured single population model with state-dependent maturity delay is formulated and analyzed. The delay is related to the size of population and taken as a non-decreasing differentiable bounded function. The model is quite different from previous state-dependent delay models in the sense that a correction term, 1-tau'(z(t))dot{z}(t), is included in the maturity rate. Firstly, positivity and boundedness of solutions are proved without additional conditions. Secondly, existence of all equilibria and uniqueness of a positive equilibrium are discussed. Thirdly, local stabilities of the equilibria are obtained. Finally, permanence of the system is analyzed, and explicit bounds for the eventual behaviors of the immature and mature populations are established.

Complex interaction of resource availability, life-history and demography determines the dynamics and stability of stage-structured populations

The dynamics of stage-structured populations facing stage-specific variability in resource availability and/or demographic factors like unequal sex-ratios, remains poorly understood. We addressed these issues using a stage-structured individual-based model that incorporates life-history parameters common to many holometabolous insects. The model was calibrated using time series data from a 49-generation experiment on laboratory populations of Drosophila melanogaster, subjected to four different combinations of larval and adult nutritional levels. The model was able to capture multiple qualitative and quantitative aspects of the empirical time series across three independent studies. We then simulated the model to explore the interaction of various life-history parameters and nutritional levels in determining population stability. In all nutritional regimes, constancy stability of the populations was reduced upon increasing egg-hatchability, critical mass, and proportion of body resource allocated to female fecundity. However, the effects of increasing sensitivity of female-fecundity to adult density on constancy stability varied across nutrition regimes. The effects of unequal sex-ratio and sex-specific culling were greatly influenced by fecundity but not by levels of juvenile nutrition. Finally, we investigated the implications of some of these insights on the efficiency of the widely-used pest control method, the Sterile Insect Technique (SIT). We show that increasing the amount of juvenile food had no effects on SIT efficiency when the density-independent fecundity is low, but reduces SIT efficiency when the density-independent fecundity is high.

Environmental oestrogens cause predation-induced population decline in a freshwater fish.

Understanding population-level effects of environmental stressors on aquatic biota requires knowledge of the direct adverse effects of pollutants on individuals and species interactions that relate to survival and reproduction. Here, we connect behavioural assays with survival trials and a modelling approach to quantify changes in antipredator escape performance of a larval freshwater fish following exposure to an environmental oestrogen, and predict changes in population abundance. We quantified the effects of short-term (21 days) exposure to 17β-oestradiol (E2) on the antipredator escape performance of larval fathead minnows (Pimephales promelas) and the probability of predation by a natural predator, the bluegill sunfish (Lepomis macrochirus). Compared with unexposed minnows, minnows exposed to environmentally relevant concentrations of E2 that approach total oestrogenic activity of wastewater-dominated environments (38 and 103 ng l−1) had delayed response times and slower escape speeds, and were more susceptible to predation. Incorporating these data into a stage-structured population model demonstrated that enhanced predation mortality at the larval stage can result in population declines. These results indicate that subtle, sub-lethal shifts in the behaviour of individuals due to human-mediated environmental change can impact species interactions with measurable population-level effects. Such changes have the potential to alter higher-order trophic interactions and disrupt aquatic communities.

A spatially explicit hierarchical model to characterize population viability.

Many of the processes that govern the viability of animal populations vary spatially, yet population viability analyses (PVAs) that account explicitly for spatial variation are rare. We develop a PVA model that incorporates autocorrelation into the analysis of local demographic information to produce spatially explicit estimates of demography and viability at relatively fine spatial scales across a large spatial extent. We use a hierarchical, spatial, autoregressive model for capture-recapture data from multiple locations to obtain spatially explicit estimates of adult survival (ϕad ), juvenile survival (ϕjuv ), and juvenile-to-adult transition rates (ψ), and a spatial autoregressive model for recruitment data from multiple locations to obtain spatially explicit estimates of recruitment (R). We combine local estimates of demographic rates in stage-structured population models to estimate the rate of population change (λ), then use estimates of λ (and its uncertainty) to forecast changes in local abundance and produce spatially explicit estimates of viability (probability of extirpation, Pex ). We apply the model to demographic data for the Sonoran desert tortoise (Gopherus morafkai) collected across its geographic range in Arizona. There was modest spatial variation in (0.94-1.03), which reflected spatial variation in (0.85-0.95), (0.70-0.89), and (0.07-0.13). Recruitment data were too sparse for spatially explicit estimates; therefore, we used a range-wide estimate ( =0.32 1-yr-old females per female per year). Spatial patterns in demographic rates were complex, but , , and tended to be lower and higher in the northwestern portion of the range. Spatial patterns in Pex varied with local abundance. For local abundances >500, Pex was near zero (<0.05) across most of the range after 100yr; as abundances decreased, however, Pex approached one in the northwestern portion of the range and remained low elsewhere. When local abundances were <50, western and southern populations were vulnerable (Pex >0.25). This approach to PVA offers the potential to reveal spatial patterns in demography and viability that can inform conservation and management at multiple spatial scales, provide insight into scale-related investigations in population ecology, and improve basic ecological knowledge of landscape-level phenomena.

Modeling the Spread of Zika Virus in a Stage-Structured Population: Effect of Sexual Transmission.

The recent Zika virus outbreak has been spreading rapidly all over the world, expanding its traditionally geographical affected regions, making it a global public health hazard and endangering millions of people. One unique property of the Zika virus compared to most vector-borne diseases is the fact that the virus is transmitted both by mosquitoes and by direct sexual contact. In the present manuscript, we formulate and analyze five mathematical compartmental models of Zika transmission. We model both transmission routes (i.e., vector-borne and sexual transmission). In order to make the model more realistic, heterogeneity in the sexual transmission is modeled in several ways. We fitted the five different models to data, inferred the parameters and selected the most appropriated model, which describes the Zika outbreak in Columbia. For all the models, we estimate the reproduction numbers, namely direct (sexual) transmission, vector transmission and the basic reproduction number [Formula: see text]. The analysis revealed that the sexual transmission contribution to [Formula: see text] is highest [15.36% (95% CI 12.83-17.4)] for the model which stratifies each gender to high-risk and low-risk individuals in their sexual behavior. For this model, the estimated [Formula: see text] is 1.89 (95% CI 1.21-2.13), the direct transmission reproduction number is 0.42 (95% CI 0.29-0.64), and the vector transmission reproduction number is 1.51 (95% CI 1.23-1.87). The sensitivity analysis demonstrated that the value of [Formula: see text] depends on three controllable parameters: the biting rate, the sexual transmission rate and the average ratio of mosquito to human.

How Long Does a Short-Lived Perennial Live? A Modeling Approach

We have composed a “scale of ontogenesis,” i.e., the sequence of ontogenetic stages, and the life cycle graph (LCG) for Androsace albana, a monocarpic plant species that is considered a short-lived perennial, according to annual observations on permanent sample plots in an alpine lichen heath during the 2009–2016 period. There is only one reproduction event in the LCG, which eliminates any reproductive uncertainty from the data of “identified individuals” type so typical for the former projects with polycarpic species, while the monocarpic cycle excludes any returns from the generative stage to a non-flowering status. The LCG describes the ontogeny through five successive stages: seedlings, juvenile, immature, adult virginal, and generative plants, the generative plants perishing after they have flowered and produced seeds. We have constructed a matrix model of the stage-structured population that corresponds to the LCG; its calibration has reduced to calculating the vital rates directly from the data of one time step, i.e., from the censuses at two successive years of observation. Therefore, the nonautonomous model represents a set of 7 annual matrices, each giving a quantitative measure of how the local population is adapted to its environment as the dominant eigenvalue of the model matrix. Its variations have turned out quite significant from year to year, signifying either a growth or decline of the local population and, in general, its vulnerability to stress factors of the environment. Averaging the annual matrices geometrically over the whole observation period has revealed the tendency to decline and enabled us to extract certain age-specific traits (in years) from the stage-structured model using the technique of virtual absorbing Markov chains and their fundamental matrices. The mean life expectancy at various stages of the A. albana ontogeny has turned out maximal in the adult virginal plants, while the mean age at flowering equal to 13 years has exceeded the horizon of the observation time series, thus proving the technique to be efficient. The model indicates that A. albana plants spend most of their life spans as virginal adults, which characterizes the space holder strategy by Korner (2003), or the delayed-development strategy by Zhukova (1995). The model outcome gives another evidence that the A. albana population is endangered.

Density feedbacks mediate effects of environmental change on population dynamics of a semidesert rodent.

Population dynamics are the result of an interplay between extrinsic and intrinsic environmental drivers. Predicting the effects of environmental change on wildlife populations therefore requires a thorough understanding of the mechanisms through which different environmental drivers interact to generate changes in population size and structure. In this study, we disentangled the roles of temperature, food availability and population density in shaping short- and long-term population dynamics of the African striped mouse, a small rodent inhabiting a semidesert with high intra- and interannual variation in environmental conditions. We parameterized a female-only stage-structured matrix population model with vital rates depending on temperature, food availability and population density, using monthly mark-recapture data from 1609 mice trapped over 9years (2005-2014). We then applied perturbation analyses to determine relative strengths and demographic pathways of these drivers in affecting population dynamics. Furthermore, we used stochastic population projections to gain insights into how three different climate change scenarios might affect size, structure and persistence of this population. We identified food availability, acting through reproduction, as the main driver of changes in both short- and long-term population dynamics. This mechanism was mediated by strong density feedbacks, which stabilized the population after high peaks and allowed it to recover from detrimental crashes. Density dependence thus buffered the population against environmental change, and even adverse climate change scenarios were predicted to have little effect on population persistence (extinction risk over 100years <5%) despite leading to overall lower abundances. Explicitly linking environment-demography relationships to population dynamics allowed us to accurately capture past population dynamics. It further enabled establishing the roles and relative importances of extrinsic and intrinsic environmental drivers, and we conclude that doing this is essential when investigating impacts of climate change on wildlife populations.

Interaction strength and stability in stage‐structured food web modules

There has been a long‐standing debate on what creates stability in food webs. One major finding is that weak interactions can mute the destabilizing potential of strong interactions. Considering that stage structure is common in nature, that existing studies on stability that include population stage structure point in different directions, and the recent theoretical developments in the area of stage structure, there is a need to address the effects of population stage structure in this context. Using simple food web modules, with stage structure in an intermediate consumer, we here begin to theoretically investigate the effects of stage structure on food web stability. We found a general correspondence to previous results such that strong interactions had destabilizing effects and weak interactions that result in decreased energy flux had stabilizing effects. However, we also found a number of novel results connected to stage structure. Interestingly, weak interactions can be destabilizing when they excite other interactions. We also found that cohort cycles and predator–prey cycles did not respond in the same way to increasing interactions strength. We found that the combined effects of two predators feeding on the same prey can strongly destabilize a system. Consistent with previous studies, we also found that stage‐specific feeding can create a refuge effect that leads to a lack of strong destabilization at high interaction strength. Overall, stage structure had both stabilizing and destabilizing aspects. Some effects could be explained by our current understanding of energetic processes; others need additional consideration. Additional aspects such as shunting of energy between stages, control of biomass fluxes, and interactions between lags and energy flux, should be considered.

Threshold Dynamics of a Temperature-Dependent Stage-Structured Mosquito Population Model with Nested Delays.

Mosquito-borne diseases remain a significant threat to public health and economics. Since mosquitoes are quite sensitive to temperature, global warming may not only worsen the disease transmission case in current endemic areas but also facilitate mosquito population together with pathogens to establish in new regions. Therefore, understanding mosquito population dynamics under the impact of temperature is considerably important for making disease control policies. In this paper, we develop a stage-structured mosquito population model in the environment of a temperature-controlled experiment. The model turns out to be a system of periodic delay differential equations with periodic delays. We show that the basic reproduction number is a threshold parameter which determines whether the mosquito population goes to extinction or remains persistent. We then estimate the parameter values for Aedes aegypti, the mosquito that transmits dengue virus. We verify the analytic result by numerical simulations with the temperature data of Colombo, Sri Lanka where a dengue outbreak occurred in 2017.

Management of invasive insect species using optimal control theory

We discuss the use of optimal control theory to determine the most cost-effective management strategies for insect pests. We use a stage-structured linear population projection model where the modeled control action increases the mortality in one of the stage-classes. We illustrate the method by using a published model for the root weevil Diaprepes abbreviatus, an invasive insect species having a substantial negative impact on citrus trees in regions such as Florida and California in the United States. Here control corresponds to the application of inundative biological control agents (entomopathogenic nematodes as biopesticides) which increases the mortality of the larval stage. Our approach determines levels and timing of control to minimize the economic loss caused by D. abbreviatus. We use two numerical methods to approximate the optimal control, and compare their effectiveness.

Codimension one and two bifurcations of a discrete stage-structured population model with self-limitation

ABSTRACTIn this paper, the bifurcations of a discrete stage-structured population model with self-limitation between the two subgroups are investigated. We explore all possible codimension-one bifurcations associated with transcritical, flip (period doubling) and Neimark-Sacker bifurcations and discuss the stabilities of the fixed points in these non-hyperbolic cases. Meanwhile, we give the explicit approximate expression of the closed invariant curve which is caused by the Neimark-Sacker bifurcation. After that, through the theory of approximation by a flow, we explore the codimension two bifurcations associated with 1:3 strong resonance. We convert the nondegenerate condition of 1:3 resonance into a parametric polynomial, and determine its sign by the theory of complete discrimination system. We introduce new parameters and utilize some variable substitutions to obtain the bifurcation curves around 1:3 resonance, which are returned to the original variables and parameters to express for easy verification. By using a series of complicated approximate identity transformations and polar coordinate transformation, we explore 1:6 weak resonance. Moreover, we calculate the two boundaries of Arnold tongue which are caused by 1:6 weak resonance and defined as the resonance region. Numerical simulations and numerical bifurcation analyzes are made to demonstrate the effective of the theoretical analyzes and to present the relations between these bifurcations. Furthermore, our theoretical analyzes and numerical simulations are explained from the biological point of view.

How to find simple nonlocal stability and resilience measures

Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the solution to jump from a safe state into another, possibly dangerous, attractor. Such phenomena cannot be traced by the widespread local stability and resilience measures, based on linearizations, accounting only for arbitrary small perturbations. Using numerical estimates of the size and shape of the basin of attraction, as well as the systems returntime to the attractor after given a perturbation, we construct simple nonlocal stability and resilience measures that record a systems ability to tackle both large and small perturbations. We demonstrate our approach on the Solow–Swan model of economic growth, an electro-mechanical system, a stage-structured population model as well as on a high-dimensional system, and conclude that the suggested measures detect dynamic behavior, crucial for a systems stability and resilience, which can be completely missed by local measures. The presented measures are also easy to implement on a standard laptop computer. We believe that our approach will constitute an important step toward filling a current gap in the literature by putting forward and explaining simple ideas and methods, and by delivering explicit constructions of several promising nonlocal stability and resilience measures.

Development of a stage-structured process-based predator–prey model to analyse biological control of cotton aphid, Aphis gossypii, by the sevenspot ladybeetle, Coccinella septempunctata, in cotton

Agricultural system diversification is well known to affect the population dynamics of crop pests, but predator–prey dynamics in crop systems are difficult to analyse due to interactions between multiple life stages of predator and prey, the modulating effect of temperature, the actions of additional predators, and the open nature of the system, with immigration and emigration of both predators and prey. To better understand and characterize the predator–prey system dynamics under field conditions, we developed a detailed process-based simulation model for the stage structured population interaction between cotton aphid, Aphis gossypii, and its main natural enemy, the sevenspot ladybeetle Coccinella septempunctata. The model includes interactions between all insects stages as affected by temperature and host growth, and was parameterized based on detailed data collection in the laboratory and the field. The model was tested with independent data. Simulations show that the initial predator–prey ratio, as affected by immigration rates of the aphid and the predators into the crop, is the key factor for biological control. The model is a useful tool for scenario assessments on the effects of crop diversification on pest-natural enemy dynamics.

Influence of body condition on the population dynamics of Atlantic salmon with consideration of the potential impact of sea lice.

Atlantic salmon Salmo salar is an iconic species of high conservation and economic importance. At sea, individuals typically are subject to sea lice infestation, which can have detrimental effects on their host. Over recent decades, the body condition and marine survival in NE Atlantic stocks have generally decreased, reflected in fewer adults returning to rivers, which is partly attributable to sea lice. We developed a deterministic stage-structured population model to assess condition-mediated population dynamics resulting in changing fecundity, age at sexual maturation and marine survival rate. The model is parameterized using data from the North Esk system, north-east Scotland. Both constant and density-dependent juvenile survival rates are considered. We show that even small sea lice-mediated changes in mean body condition of MSW can cause substantial population declines, whereas 1SW condition is less influential. Density dependence alleviates the condition-mediated population effect. The resilience of the population to demographic perturbations declines as adult condition is reduced. Indirect demographic changes in salmonid life-history traits (e.g., body condition) are often considered unimportant for population trajectory. The model shows that Atlantic salmon population dynamics can be highly responsive to sea lice-mediated effects on adult body condition, thus highlighting the importance of non-lethal parasitic long-term effects.